Is it possible to animate a single mesh with multiple armatures at once?
You can't parent a mesh to multiple armatures, but you can have multiple armatures deforming a single mesh. As armatures can have multiple bones, it wouldn't normally be needed.

I don't think that any of the following will export to Unreal or Unity, so this would only relate to animations to be rendered using blender  -

Parenting the armatures to each other will only move them together in object mode. Within blender, you could use a child of constraint to have multiple armatures move as one in pose mode when desired, you can animate the influence to turn it on/off. This also allows you to parent it to different armatures or bones at different times. Other constraints may also give a desired result.



For an object, you can add as many armature modifiers as you want, each modifier then uses a different armature. Instead of using the Parent->Armature Deform options, you will want to add and set each modifier manually. The catch is that the bone names are used to link bones to which vertex groups they move, unless you are using bone envelopes, that means the armatures will need to use unique bone names between them or multiple bones will move the same vertices.